Details

sample112.0ms

Algorithm

intervals

Results

37.0ms	86×	body	1280	valid
25.0ms	68×	body	640	valid
19.0ms	247×	body	80	valid
7.0ms	33×	body	320	valid
3.0ms	17×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	105	13
1	105	13

prune14.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.3b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
0.4b	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`times-frac`
32×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-r` `sqrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1` `add-log-exp`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

3 → 94

Calls

3 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
10.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
7.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series54.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
38.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
11.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4961	1529
1	4961	1529

prune174.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	95	10	105

Merged error: 0b

Counts

105 → 10

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(* (+ (* a1 a1) (* a2 a2)) (cos th))
0.4b	(/ (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 2.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`times-frac` `associate-/r*` `sqrt-prod`
5×	`pow1` `add-log-exp`
4×	`associate-*l/`
3×	`flip3-+` `associate-r` `associate-l` `flip-+`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `frac-2neg` `pow-prod-down` `clear-num` `sum-log` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 60

Calls

3 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
6.0ms	(* (+ (* a1 a1) (* a2 a2)) (cos th))
8.0ms	(/ (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 2.0))

series49.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
16.0ms	(* (+ (* a1 a1) (* a2 a2)) (cos th))
27.0ms	(/ (* (+ (* a1 a1) (* a2 a2)) (cos th)) (sqrt 2.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4990	841
1	4990	841

prune109.0ms

Filtered

48 candidates to 69 candidates (-43.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	71	8	79

Merged error: 0b

Counts

79 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.3b	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))
0.3b	(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`sqrt-prod`
1119×	`times-frac`
625×	`add-sqr-sqrt`
578×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-r`
34×	`associate-/l*`
22×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
13×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
3×	`associate-l` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`+-commutative` `associate-r/` `pow-prod-down` `sum-log` `-commutative`

Counts

4 → 713

Calls

4 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
68.0ms	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
9.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))
18.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
36.0ms	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
14.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0)))
20.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify155.0ms

Algorithm

egg-herbie

Counts

725 → 725

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5149	16199

prune783.0ms

Filtered

251 candidates to 725 candidates (-188.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	722	3	725
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	727	6	733

Merged error: 0b

Counts

733 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0))))
0.4b	(* (* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0))) (cos th)) (/ (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))))
6.6b	(sqrt (+ (* a1 a1) (* a2 a2)))
6.6b	(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite429.0ms

Algorithm

rewrite-expression-head

Rules

6360×	`sqrt-prod`
3624×	`times-frac`
1846×	`add-sqr-sqrt`
1844×	`add-cube-cbrt` `*-un-lft-identity`
916×	`associate-r`
76×	`associate-/l*`
45×	`add-exp-log` `add-cbrt-cube`
27×	`div-inv`
15×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
12×	`associate-/r*`
11×	`pow1`
4×	`sqrt-div` `add-log-exp`
3×	`pow-prod-down` `associate-*l/`
2×	`rem-sqrt-square` `sqrt-undiv` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative` `associate-/l/`

Counts

4 → 1994

Calls

4 calls:

43.0ms	(/ (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0))))
157.0ms	(* (* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0))) (cos th)) (/ (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0))))
26.0ms	(* (* (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0))) (cos th)) (/ (/ (sqrt (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms	(sqrt (+ (* a1 a1) (* a2 a2)))

simplify739.0ms

Algorithm

egg-herbie

Counts

2006 → 2006

Iterations

Useful iterations: 0 (202.0ms)

Iter	Nodes	Cost
0	4985	62342
1	4985	62342

prune2.0s

Filtered

378 candidates to 2006 candidates (-430.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	2006	0	2006
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	2006	6	2012

Merged error: 0b

Counts

2012 → 6

regimes356.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	34
1	20	34

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	2577×	body	1280	valid
636.0ms	2125×	body	640	valid
574.0ms	7962×	body	80	valid
223.0ms	990×	body	320	valid
80.0ms	541×	body	160	valid

Details

sample112.0ms

simplify4.0ms

prune14.0ms

localize10.0ms

rewrite23.0ms

series54.0ms

simplify49.0ms

prune174.0ms

localize10.0ms

rewrite19.0ms

series49.0ms

simplify48.0ms

prune109.0ms

localize12.0ms

rewrite153.0ms

series76.0ms

simplify155.0ms

prune783.0ms

localize17.0ms

rewrite429.0ms

series51.0ms

simplify739.0ms

prune2.0s

regimes356.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.2s

Profiling